Sony introduced the ability to remote play with the PS4 on Android but it was limited to Sony Xperia devices only. However with Android being a very hack friendly OS, developers have been able to modify the original Remote Play app to work on most Android devices that are running Android 4.4 and above.
Here are the steps to install Remote Play on your Android device.
1. Download and install this APK on your Android device.
2. Once installed, open the app and sign in with your PSN account.
3. Your controller will automatically disconnect. Press the PSN button on it and use the secondary PSN account you should see, next to your main one. It'll most probably have the same name but without a user icon.
Now you should be all connected and ready to play!
You will notice some lag which is inevitable. The only way to reduce lag is to stay connected to the same WiFi network and use a powerful router. I would advise against trying to play online games that require quick input such as Call of Duty.